Real-time models of electrostatically actuated cantilever probes with integrated thermal sensor for nanoscale interrogation

Microcantilevers with integrated thermal sensor for topography measurement, which can be electrostatically actuated, are well suited for a highly parallel dynamic-mode operation where multiple cantilevers scan the media. Interpretation of data in dynamic-mode operation utilizing such cantilevers is complex because of diverse forces acting on the cantilever that include electrostatic, interatomic, structural, thermal, and, possibly, magnetic forces. In addition, the thermal sensor introduces new dynamics making interpretation of measured data challenging. In this paper, tractable models that are suited for real-time purposes, which can quantitatively predict the cantilever motion and the thermal-sensor measurement, are presented. Furthermore, it is demonstrated that all parameters of the model can be estimated solely from thermal-sensor data. This paper also provides a comprehensive understanding of the dynamics of the thermal sensor.